Question

Write an equation in slope-intercept form of the line with the parametric equations x=9t and y=4t+2 .

Answer 1

`9t=x\qquad\text{divide both sides by 9}\\\\t=(x)/(9)\to t=(1)/(9)x\\\\\text{substitute to}\ y=4t+2\\\\y=4\left((1)/(9)x\right)+2\\\\\boxed{y=(4)/(9)x+2}`

Answer 2

The required equation in slope-intercept form is
`y=(4)/(9)x+2`

Explanation:

Given : The parametric equations
`x=9t` and
`y=4t+2`

To find : Write an equation in slope-intercept form of the line?

Solution :

The parametric equations were re-written in terms of t is

`t=(x)/(9)`

and
`t=(y-2)/(4)`

Now, equating both t we get,

`(x)/(9)=(y-2)/(4)`

`4x=9(y-2)`

`4x=9y-18`

Separate y from the equation to form slope-intercept form

`4x+18=9y`

`y=(4x+18)/(9)`

`y=(4x)/(9)+2`

The slope intercept form is
`y=mx+b`

where, m is the slope of line and b is the y-intercept.

So, The required equation in slope-intercept form is
`y=(4)/(9)x+2`